1. Field of the Invention
This invention relates generally to a system and method for estimating a surface coefficient of friction and, more particularly, to a system and method for estimating a surface coefficient of friction in a vehicle system by calculating a ratio of measured force to maximum force when an error between the estimated and measured front and rear axle lateral velocity difference is larger than a minimum threshold.
2. Discussion of the Related Art
Vehicle stability control systems are known in the art to enhance vehicle stability in the event that the system detects that the vehicle may not be operating as the driver intends. For example, on an icy or snowy surface, the driver may steer the vehicle in one direction, but the vehicle may actually travel in another direction. Signals from various sensors, such as yaw-rate sensors, hand-wheel angle sensors, lateral acceleration sensors, etc., can detect the vehicle instability. Calculations made by these types of vehicle stability control systems often require an estimation of the vehicle's lateral velocity and/or the surface coefficient of friction. Typically, it is necessary to know at least some assumption of the surface coefficient of friction to estimate the vehicles lateral velocity. The estimation of the surface coefficient of friction based on a lateral acceleration is typically not robust relative to a banked curve because of the gravity bias effect on the body mounted lateral accelerometer.
Estimation of a vehicle's lateral velocity, or vehicle side-slip angle, has been a research subject for many years. Known work has shown the performance of four different methods to estimate side-slip angle. These methods include the integration of a lateral acceleration signal, with and without a “washout” filter, a simple algebraic approach and a non-linear observer with and without measurement update, sometimes referred to as an output injection. Other work combined a model-based observer with direct integration of vehicle kinematic equations based on weights determined by the degree of a nonlinear state of the vehicle. The nonlinear state of the vehicle is established by the deviation of the yaw-rate from a predetermined reference value. The resulting observer utilizes an estimate of surface coefficient of friction and road bank angle to maintain accuracy and robustness. Other work demonstrated the performance of an extended Kalman filter based on the single track bicycle model. The estimation of surface coefficient of friction is based on a least squares regression of the difference between the actual and tire model-based lateral forces. The stability of the proposed observer on banked roads and in the presence of sensor bias was not addressed. Other work proposed two nonlinear observers based on a two track vehicle model. The proposed observers use the estimation of cornering stiffness from a nonlinear least squares technique.
Current production yaw stability control systems do not rely directly on feedback control of lateral velocity or side-slip angle estimates because a production level robust and accurate estimate of lateral velocity has not been fully developed. However, production yaw stability control systems do utilize an estimate of a vehicle's lateral velocity to influence or modify the yaw-rate error used for feedback control. The lateral velocity estimate can influence the yaw control strategy, but typically only when a non-zero yaw-rate error is calculated. In general, there are dynamic conditions in which the vehicle develops a side-slip angle that the yaw stability controller will not detect and stabilize. When the vehicle develops large side-slip angles, it becomes less responsive to steering input and more difficult for the driver to control. This can happen, for example, during open loop steering maneuvers on low coefficient of friction surfaces. During an open loop steering maneuver, the driver inputs a ramp steer up to 90° and holds the steering wheel angle. While such maneuvers might seem unreasonable because they require the driver not to correct a possible vehicle over-steer behavior, it cannot be assumed that all drivers would know when and how to counter-steer the vehicle out of the unstable condition. Any instance in which the vehicle's side-slip angle increases to a relatively large level for a given surface the driver may have trouble controlling the vehicle. Standard stability control systems allow the estimation of lateral velocity to rely only on the use of yaw-rate, lateral acceleration, steering wheel angle, and wheel speed sensor measurements. The estimation of lateral velocity also requires an estimate of the lateral surface coefficient of friction.